Problem: Simplify the following expression: $q = \dfrac{-8x - 9}{6x + 2} - \dfrac{-8x - 1}{6x + 2}$
Solution: Since the expressions have the same denominator we simply subtract the numerators: $q = \dfrac{-8x - 9 - (-8x - 1)}{6x + 2}$ Distribute the negative sign: $q = \dfrac{-8x - 9 + 8x + 1}{6x + 2}$ Combine like terms: $q = \dfrac{-8}{6x + 2}$ Simplify by dividing numerator and denominator by 2: $q = \dfrac{-4}{3x + 1}$